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Grade: 12 
        
Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number". 


Statement-1 : 

r is equivalent to either q or p. 


Statement-2 : 

r is equivalent to ~(p ↔ ~q).
9 years ago

Answers : (1)

ronit bhatiya
14 Points 
							
p : x is an irrational number 

q : y is a transcendental number  

r : x is a rational number iff y is a transcendental number  

=> r : ~ p ↔ q   

s1 : q or p   

s2 : ~ (p↔~q)  







    
        

            p
            q
            ~p
            ~q
            r:~p↔q
            s1:q or p
            p↔~q
            s2:~(p↔~q)

            		
        

        

            T
            T
            F
            F
            F
            T
            F
            T
        

        

            T
            F
            F
            T
            T
            T
            T
            F
        

        

            F
            T
            T
            F
            T
            T
            T
            F
        

        

            F
            F
            T
            T
            F
            F
            F
            T
        

    




Based upon above chart 

s1 and r are not equivalent 

s2 and r are not equivalent
9 years ago
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